I don't believe the temp solution is viable for this reason. Yes, you can raise the temp which will accelerate the life cycle of ick, but to KILL it, the temp would have to be raised to such a level that you would also kill the fish and whatever else is in the tank.
Yes, ick is a parasitic partner with fish; however, in their natural environment, this does not pose a big problem because the fish can escape infestation by virture of large volumes of water and fish. Most parasites don't want to kill their hosts, because if they did then they would also end up killing themselves off too.
However, in the capative aquaria both ick and fish have a problem. There are very limited fish in the aquarium, and there is no escape for fish. The ick is captured just as the fish are and they proliferated, and proliferate, and proliferate, in the closed confines of the tank. Ick must feed and have a very limited amt of fish to feed on. Therein is the problem for fish in the aquairum.
Look at ick as being to fish what flees are to mammals. Animals in the wild have flees but usually have no ill effects from them. However, take that animal & put them in a cage or make it a house pet and then you have a problem. You must get rid of the flees or the animal will suffer, and could even die from flee investation.
Heres how ick works:
Saltwater ich are found in nature and normal, healthy fish commonly carry a few of these parasites when collected. Left in the ocean, fish will experience no real ill effects from ick unless some other stressor is present---for instance an injury to the fish. Once captured, however, stressors to fish are extreme [please see TerryB’s series on stress in the Fish Forum] and the fish become vulnerable to parasitic infestation. Thus, a parasite that causes little trouble in the wild, becomes a menace in the captive environment.
Most find that there is no effective treatment for ick as long as the parasites remain embedded in the fish; some, however, purport that FW dips are an effective initial treatment of ick [while the parasites are embedded in the host fish] to be followed by other, longer term conventional treatments, such as hyposalinity or copper treatment. The standard treatment for ick is hyposalinity or use of copper. My preference is hyposalinity.
Ick has a life cycle of approx. 23 days during which time the parasite undergoes 3 stages. In the tomite [free-swimming] stage, the parasite is infectious to fish. During this stage, the tomite’s goal is to find a host fish, or die trying. In the aquarium, tomites have no problem finding a host. After they attach to the gills or body of a fish, they develop into the second stage, the parasitic trophont. During this stage they burrow into the fish, feeding on it’s tissues, which can cause considerable damage and even result in a secondary bacterial infection on the infected fish. Once well fed the trophonts stop feeding and develop cystic coverings. This becomes the inactive tomont stage and during this final stage the cysts may stay trapped in the mucus of the fish, or fall off and sit on the bottom of the aquarium. Within 6 to 10 days hundreds of new tomites emerge looking for fish hosts and the cycle begins all over again, and again and again until something is done about it. Once ick is an active presence in the aquaria, having infested fish, it must be irradiated or it will always pose a threat to fish, and to any new fish introduced. The only time this parasite is vulnerable is during their free swimming stage [unless you are a hobbyist who strongly believes in FW dips & that ick are also effected by dips]. The standard treatment for Ick is copper sulfate and hyposalinity. Only in the free-swimming stage are these 2 treatments effective.
The parasite must feed, and your fish is the food source. May a fish survive ick? Yes it might, for awhile. However, every 3 weeks ick will attack fish so it can feed.
You do not need to medicate with ick. Use hyposalinity. However, since you have inverts and LR, you will have to do this in a separate tank. If you absolutely can't do this, I would suggest getting a cleaner shrimp and using garlic soaked food. That would be better than doing nothing, but it will not eliminate ick from your tank.